Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

100 Incompressible laminar ¯ow
1.5
–0.01
1.0
'CBS'
–0.02
–0.03
'CBS'
0.5
–0.04
–0.05
0
–0.06
–0.07
–0.5
–0.08
–1.0
–0.09
–0.10
–1.5
0 0.2 0.4 0.6 0.8 1.0
–0.11
0 0.2 0.4 0.6 0.8 1.0
x1 x1 (a) Stokes flow, viscosity 1
(b) Re = 400
p
As we have mentioned in Chapter 3, it is important when using explicit procedures
to make sure that the damping introduced is su cient for ensuring that
an oscillation-free solution can be obtained. With the explicit algorithm the time
steps will inevitably be small as they are governed by the compressible wave velocity.
It is convenient here, and indeed sometimes essential, to introduce the internal t int
which is di€erent from the external t ext. This matter is discussed by Nithiarasu
et al. in reference 10 where several examples are shown proving the e€ectiveness
of this process.
4.4 Boundary-exit conditions
p
–0.02
–0.02
–0.03
'CBS'
–0.03
'CBS'
–0.04
–0.04
–0.05
–0.05
–0.06
–0.07
–0.06
–0.08
–0.07
–0.09
–0.08
–0.10
–0.09
–0.11
0 0.2 0.4 0.6 0.8 1.0
–0.10
0 0.2 0.4 0.6 0.8 1.0
x1 x1 (c) Re = 1000
(d) Re = 5000
p
p
Fig. 4.5 Lid-driven cavity. Pressure distribution along horizontal mid-plane for different Reynolds numbers
(semi-implicit form).
The exit boundary conditions described in the previous chapter (Chapter 3, Sec. 3.6)
are tested here for ¯ow past a backward facing step. The geometry and boundary
conditions are shown in Fig. 4.10(a). Figures 4.10 and 4.11 show the results obtained
using the exit boundary conditions discussed in Chapter 3. For the sake of